An arithmetic progression is $a+0b, a+1b, a+2b, ..., a+nb$
A geometric progression is $ab^0, ab^1, ab^2, ..., ab^n$.
Multiplication is arithmetic, so why is a geometric progression not also an "arithmetic" progression?
A line being extended be iteratively adding a constant length is a geometric construction, so why is an arithmetic progression not also a "geometric" progression?